Introduction to Statistical Physics

Intended for beginning graduate students or advanced undergraduates, this text covers the statistical basis of equilibrium thermodynamics, both classical and quantum, including examples from solid-state physics. It also treats some topics of more recent interest such as phase transitions and non-equilibrium phenomena. The approach to equilibrium statistical mechanics is based on the Gibbs microcanonical ensemble. The presentation introduces modern ideas, such as the thermodynamic limit and the equivalence of ensembles, and uses simple models (ideal gas, Einstein solid, ideal paramagnet) to make the mathematical ideas clear. Frequently used mathematical methods are reviewed in an appendix. The book begins with a review of statistical methods and classical thermodynamics, making it suitable for students from a variety of backgrounds. Classical thermodynamics is treated in the in the context of the classical ideal gas and the canonical and grand canonical ensembles. The discussion of quantum statistical mechanics includes Bose and Fermi gases. the Bose-Einstein condensation, phonons and magnons. Phase transitions are first treated classically (using the van der Waals and Curie-Weiss phenomenological models as examples), and then quantum mechanically (the Ising model, scaling theory and renormalization). The book concludes with two chapters on nonequilibrium phenomena: one using Boltzmann's approach, the other based on stochastic models. Exercises at the end of each chapter are an integral part of the course, clarifying and extending topics discussed in the text. Hints and solutions can be found on the author's web site.

Table of Contents:
1 Introduction to Statistical Methods.- 2 Statistical Description of a Physical System.- 3 Overview of Classical Thermodynamics.- 4 Microcanonical Ensemble.- 5 Canonical Ensemble.- 6 The Classical Gas in the Canonical Formalism.- 7 The Grand Canonical and Pressure Ensembles.- 8 The Ideal Quantum Gas.- 9 The Ideal Fermi Gas.- 10 Free Bosons: Bose—Einstein Condensation; Photon Gas.- 11 Phonons and Magnons.- 12 Phase Transitions and Critical Phenomena: Classical Theories.- 13 The Ising Model.- 14 Scaling Theories and the Renormalization Group.- 15 Nonequilibrium Phenomena: I. Kinetic Methods.- 16 Nonequilibrium phenomena: II. Stochastic Methods.- Appendices.- A.1 Stirling’s asymptotic series.- A.2 Gaussian integrals.- A.3 Dirac’s delta function.- A.4 Volume of a hypersphere.- A.5 Jacobian transformations.- A.6 The saddle-point method.- A.7 Numerical constants.